PTT 201/4 THERMODYNAMIC SEM 1 ( 2013/2014). CHAPTER 7: Entropy. Objectives. • Apply the second law of thermodynamics to processes. • Define a new property called entropy to quantify the second- law effects. • Calculate the entropy changes that take place during.
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PTT 201/4THERMODYNAMIC
SEM 1 (2013/2014)
Objectives
• Apply the second law of thermodynamics to processes.
• Define a new property called entropy to quantify the second-law effects.
• Calculate the entropy changes that take place during
processes for pure substances, incompressible substances,and ideal gases.
• Examine a special class of idealized processes, called
isentropic processes, and develop the property relations forthese processes.
• Derive the reversible steady-flow work relations
• Introduce and apply the entropy balance to various systems.
2
WHAT IS ENTROPY?
A measure of molecular disorders ormolecular randomness in a system
The larger value of S, the more molecular randomness of particles in the system
The level of molecular
disorder (entropy) of substance increases asit melts or evaporates.
The paddle-wheel work done on a gas increases the level ofdisorder (entropy) of the gas, and thus energy is degradedduring this process.
During a heat
In the absence of
transfer process, the
friction, raising aweight by a rotating
net entropy
increases. (Theincrease in the
shaft does not
create any disorder(entropy), and thusenergy is not
entropy of the coldbody more than
offsets the decrease
degraded during thisprocess.
in the entropy of
the hot body.)4
ENTROPY (How to measure the entropy-
based-on from Clausius inequality)
Clasius
inequality
Formal
definitionof entropy
The system considered inthe development of theClausius inequality.
The equality in the Clausius inequality holdsfor totally or just internally reversible cyclesand the inequality for the irreversible ones.
(based-on energy balance)
5
The entropy change between two
specified states is the same whether
the process is reversible or irreversible.
∆S can be positive/negative depending on the direction of heat transfer:
Q transfer to a system: ∆S increase (+ve)
Q transfer from a system: ∆S decrease (-ve)
A Special Case: Internally ReversibleIsothermal Heat Transfer Processes
This equation is particularly useful for determiningthe entropy changes of thermal energy reservoirs at constant temperature.
6
A piston-cylinder device contains a liquid-vapor mixture of water at 300 K. During a constant pressure process, 750 kJ of heat is transferred to the water. As a result, part of the liquid in the cylinder vaporizes. Determine entropy change of the water during this process
Some Remarks about Entropy
1.Processes can occur in a certaindirection only, not in any
direction. A process must proceed in the direction thatcomplies with the increase of entropy principle, that is, Sgen ≥
0. A process that violates this principle is impossible.
2.Entropy is a nonconserved property, and there is no such
thing as the conservation of entropy principle. Entropy isconserved during the idealized reversible processes only andincreases during all actual processes.
3.The performance of engineering systems is degraded by the
presence of irreversibilities, and entropy generation is ameasure of the magnitudes of the irreversibilities during thatprocess. The greater the extent of irreversibilities, the
greater the entropy generation. It is also used to
establish criteria for the
performance of engineering devices.
7
A heat source at 800 K losses 2000 kJ of heat to a sink at (a) 500 K and (b) 750 K. Determine which heat transfer process is more irreversible.
ENTROPY CHANGE OF PURE SUBSTANCES
Entropy is a property, and thus thevalue of entropy of a system is fixedonce the state of the system is fixed.
Schematic of the T-s diagram for water.
Entropy change
The entropy of a pure substanceis determined from the tables
(like other properties).
8
Where m is specified mass
A rigid tank contains 5 kg of refrigerant-134a initially at 20˚C and 140 kPa. The refrigerant is now cooled while being stirred until its pressure drops to 100 kPa. Determine the entropy change of the refrigerant during this process.
ISENTROPIC PROCESSES
A process during which the entropy remains constant is calledan isentropic process.
During an internally
reversible, adiabatic
(isentropic) process, theentropy remains constant.
The isentropic process appears as avertical line segment on a T-s diagram.
9
Steam enters an adiabatic turbine at 5 MPa and 450˚C and leaves at a pressure of 1.4 MPa. Determine the work output of the turbine per unit mass of steam if the process is reversible.
ENTROPY CHANGE OF LIQUIDS AND SOLIDS (INCOMPRESSIBLE SUBSTANCES)
Derived from
equation 7-23,
Liquids and solids can beapproximated as
or known asGibbs equation
incompressible substances
since their specific volumesremain nearly constant
during a process.
For an isentropic process of an incompressible substance
10
Liquid methane is commonly used in various cryogenic applications. The critical temperature of methane is 191 K to keep it in liquid phase. The properties of liquid methane at various temperatures and pressures are given in Table 7-1. Determine the entropy change of liquid methane as it undergoes a process from 110 K and 1 MPa to 120 K and 5 MPa (a) using tabulated properties and (b) approximating liquid methane as an incompressible substance. What is the error involved in the latter case?
THE ENTROPY CHANGE OF IDEAL GASES
From the first T ds relation (Eq 7-25). From the second T dsrelation (Eq 7-26)
Ideal gas
properties
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Constant Specific Heats (Approximate Analysis)
Entropy change of an ideal gas on a
unit-mole basis
Under the constant-specific-
heat assumption, the specificheat is assumed to be constantat some average value.
12
Variable Specific Heats (Exact Analysis)
We choose absolute zero as the reference
temperature and define a function s° as
On a unit-mass basis
The entropy of an ideal
gas depends on both T
and P. The function sorepresents only the
On a unit-mole basis
temperature-dependent
part of entropy.
13
Air is compressed from an initial state of 100 kPa and 17˚C to a final state of 600 kPa and 57˚C. Determine the entropy change of air during this compression process by using (a) property values from the air table and (b) average specific heats.
Isentropic Processes of Ideal Gases
Constant Specific Heats (Approximate Analysis)
Setting this eq. equal to
zero, we get
The isentropic relations of idealgases are valid for the isentropicprocesses of ideal gases only.
15
Isentropic Processes of Ideal Gases
Variable Specific Heats (Exact Analysis)
Relative Pressure and Relative Specific Volume
The use of Prdatafor calculating the
exp(s°/R) isthe relativepressure Pr.
final temperatureduring an isentropicprocess.
Refer Table A-17
Pv=RT (ideal gas relationship),
R=constant
The use of vrdata for
calculating the finaltemperature during an
T/Pris the relativespecific volume vr.
isentropic process
1
Helium gas is compressed by an adiabatic compressor from an initial state of 100 kPa and 10˚C to a final temperature of 160˚C in a reversible manner. Determine the exit pressure of helium.
TRY EXAMPLE 7-10
REVERSIBLE STEADY-FLOW WORK
From energy balance
for steady-state device
(- sign means work is produced by the system)
When kinetic and
potential energiesare negligible
(+ sign means work is done on the system)
The larger the
specific
volume, thegreater thework
For the steady flow of a liquid through adevice that involves no work interactions(such as a pipe section), the work term iszero (Bernoulli equation):
Reversible workrelations for steady-flow and closedsystems.
produced (orconsumed) bya steady-flowdevice.
17
Determine the compressor work input required to compress stem isentropically from 100 kPa to 1 MPa, assuming that the steam exists as (a) saturated liquid and (b) saturated vapor at the inlet state.
ENTROPY BALANCE
Entropy Change of a
System, ∆Ssystem
Energy and entropybalances for a system
Mechanisms of Entropy Transfer, Sin and Sout
1 Heat Transfer
Entropy transfer by heat transfer:
Entropy transfer by work:
Heat transfer is always accompanied byentropy transfer in the amount of Q/T,where T is the boundary temperature.
No entropy accompanies work as it crossesthe system boundary. But entropy may begenerated within the system as work is
dissipated into a less useful form of energy.20
2 Mass Flow
Entropy transfer by mass:
When the properties of the masschange during the process
Mass contains entropy as well asenergy, and thus mass flow into or
out of system is always
accompanied by energy andentropy transfer.
21
Entropy Generation, Sgen
Entropy generationoutside system
boundaries can beaccounted for by
writing an entropy
balance on an
extended system thatincludes the system
and its immediate
surroundings.
Mechanisms of entropy transfer for ageneral system.
2
Closed Systems
The entropy change of a closed system during a process is equal to thesum of the net entropy transferred through the system boundary by heat
transfer and the entropy generated within the system boundaries.
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Control Volumes
The entropy of a
substance alwaysincreases (or
remains constant in
The entropy of a controlvolume changes as a resultof mass flow as well as heattransfer.
the case of a
reversible process)as it flows through asingle-stream,
adiabatic, steady-
flow device.
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Try the examples in the next slides
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